The turbulent dynamo

Tobias, Steven M.

doi:10.1017/jfm.2020.1055

Cited by 74 publications

(44 citation statements)

References 185 publications

(327 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This effect was first considered by Eymin and Hulot (2005); Pais and Jault (2008) in the context of core flow inversions. For a more general discussion of the effects of the MHD turbulence in dynamos, we refer to Nataf and Schaeffer (2015) and Tobias (2021). Small-scale flows can be defined based on the length scale at which the Lorentz force dominates the Coriolis force, typically observed for n ≥ 13 (Aubert 2019;Aubert and Gillet 2021).…”

Section: Insights Into Core Flow and Dynamicsmentioning

confidence: 99%

A Dynamical Prospective on Interannual Geomagnetic Field Changes

2021

View full text Add to dashboard Cite

Geomagnetic observations from satellites have highlighted interannual variations in the rate of change of the magnetic field originating from Earth's core. Downward continued to the core surface, these variations primarily show up in the equatorial belt. First, we recall the main characteristics of these patterns, addressing their spatio-temporal resolution, as seen from field models. We then review the several dynamical frameworks proposed so far to understand and model these observations, which populate the frequency spectrum on time scales close to the Alfvén time A ≈ 2 yr, much shorter than the vortex turnover time U ≈ 150 yr in Earth's core. Magnetic-Archimedes-Coriolis (MAC) waves in a stratified layer below the core surface constitute a first possibility in the case of a sub-adiabatic heat flux at the top of the core. Their period may reach the interannual range for a layer thickness less than ≈ 30 km, for a buoyancy frequency of the order of the Earth's rotation rate. An alternative has been proposed in a context where the Coriolis force dominates the momentum balance, rendering transient motions almost invariant along the rotation axis (quasi-geostrophy, QG). Torsional Alfvén waves, consisting of axisymmetric QG motions, operate at periods similar to the Alfvén time, but are not sufficient to explain the interannual field changes, which require non-axisymmetric motions. QG Alfvén waves (involving the Coriolis and magnetic forces) constitute another possibility, with inertia playing an important role. They have been detected in the latest generation of geodynamo simulations, propagating in a ubiquitous manner at a speed slightly less than the Alfvén velocity. They are localized in longitude and as a result their description requires high azimuthal wavenumber. But the branch of QG waves with large extent in azimuth is also worth considering, as it reaches interannual periods as their radial wavenumber is increased. The excitation of such high-frequency dynamics is discussed with respect to the temporal spectrum of the core field, which presents a slope ∼ f −4 for periods approximately between A and U . We finally summarize the main geophysical implications of the existence of this interannual dynamics on core and lower mantle structure, properties, and dynamics.

show abstract

Section: Insights Into Core Flow and Dynamicsmentioning

confidence: 99%

A Dynamical Prospective on Interannual Geomagnetic Field Changes

2021

View full text Add to dashboard Cite

show abstract

“…This phenomenon has been amply reviewed, in terms for example of the so-called alpha-dynamos, in many papers and books (see [34,35], and e.g. [36,37] for references). Similarly, magnetic helicity is involved in the saturation (and possibly the enhancement) mechanism of the large-scale dynamo when the magnetic field is strong enough to react on the velocity [38].…”

Section: A Brief Mention Of Helical and Non-helical Dynamosmentioning

confidence: 99%

Helical fluid and (Hall)-MHD turbulence: a brief review

Pouquet

Yokoi

2022

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main features, both new and old, such as the discovery of bi-directional cascades or the role of helical vortices in the enhancement of large-scale magnetic fields in the dynamo problem. The dynamical contribution in magnetohydrodynamic of the cross-correlation between velocity and induction is discussed as well. We consider next how turbulent transport is affected by helical constraints, in particular in the context of magnetic reconnection and fusion plasmas under one- and two-fluid approximations. Central issues on how to construct turbulence models for non-reflectionally symmetric helical flows are reviewed, including in the presence of shear, and we finally briefly mention the possible role of helicity in the development of strongly localized quasi-singular structures at small scale. This article is part of the theme issue ‘Scaling the turbulence edifice (part 2)’.

show abstract

“…However, the need for a description on a vast range of spatial and temporal scales means that the pertinent parameter regime lies far beyond the capabilities of even modern supercomputers (e.g. [1]). For this reason, alternative approaches and descriptions are being investigated.…”

Section: Introductionmentioning

confidence: 99%

Direct statistical simulation of low-order dynamosystems

Marston

Tobias

2021

Proc. R. Soc. A.

View full text Add to dashboard Cite

In this paper, we investigate the effectiveness of direct statistical simulation (DSS) for two low-order models of dynamo action. The first model, which is a simple model of solar and stellar dynamo action, is third order and has cubic nonlinearities while the second has only quadratic nonlinearities and describes the interaction of convection and an aperiodically reversing magnetic field. We show how DSS can be used to solve for the statistics of these systems of equations both in the presence and the absence of stochastic terms, by truncating the cumulant hierarchy at either second or third order. We compare two different techniques for solving for the statistics: timestepping, which is able to locate only stable solutions of the equations for the statistics, and direct detection of the fixed points. We develop a complete methodology and symbolic package in Python for deriving the statistical equations governing the low-order dynamic systems in cumulant expansions. We demonstrate that although direct detection of the fixed points is efficient and accurate for DSS truncated at second order, the addition of higher order terms leads to the inclusion of many unstable fixed points that may be found by direct detection of the fixed point by iterative methods. In those cases, timestepping is a more robust protocol for finding meaningful solutions to DSS.

show abstract

The turbulent dynamo

Abstract: Abstract

Cited by 74 publications

References 185 publications

A Dynamical Prospective on Interannual Geomagnetic Field Changes

A Dynamical Prospective on Interannual Geomagnetic Field Changes

Helical fluid and (Hall)-MHD turbulence: a brief review

Direct statistical simulation of low-order dynamosystems

Contact Info

Product

Resources

About